Tinned wire is normally used for off shore boats.
In fresh water you rarely see it. 10 years later a non-tinned 4-gauge cable going into a distribution block shows no signs of oxidation.
We crimp and solder on nickel plated lugs so essentially the exposed part of the wire is tinned.
Don't worry about 'tinned' wire. Worry more about lugs with cheap coatings and cheap wire that isn't cooper.

DMC - I'd say no to the tinned wire. Oxidation will vary a lot depending on what part of the country you are in. The larger issue is getting legit cables in the first place. A few years back many accessory companies tried to save a few bucks on their product costs by significantly undersizing the power cable core and also substituting CCA from old fashioned copper. They figured consumers wouldn't notice this change. And frankly, many don't. It don't make it right for your system by a long shot.

My advice is find real copper cables and not worry about the tinned aspect. If you need help with which brands to stay away from, PM me. I'll share more specific info. Also price is a huge factor here. Real copper costs 2-3x the CCA stuff.

My '01 Malibu spent its first 10 years on a covered lift with the original owner (I keep it garaged year-round). No tinned wire from the factory and even the power/ground lugs were not tinned, no corrosion issues at all.

I did go with tinned lugs this time, but just because I found a good deal on them.